Abstract
Deadlock avoidance is a key issue in wormhole networks. A first approach [9] consists in removing the cyclic dependencies between channels. Although the absence of cyclic dependencies is a necessary and sufficient condition for deadlock-free deterministic routing, it is only a sufficient condition for deadlock-free adaptive routing. A more powerful approach [12] only requires the absence of cyclic dependencies on a connected channel subset. Moreover, we proposed a necessary and sufficient condition for deadlock-free adaptive routing [15].
In this paper, we design adaptive routing algorithms for k-ary n-cubes. In particular, we propose partially adaptive and fully adaptive routing algorithms which considerably increase the throughput achieved by the deterministic routing algorithm. Also, we evaluate the performance of the new routing algorithms under both, uniform and non-uniform distribution of message destinations.
This work was supported by the Spanish CICYT under Grant TIC91-1157-C03-03
Preview
Unable to display preview. Download preview PDF.
References
A. Agarwal, “Limits on interconnection network performance”, IEEE Trans. Parallel Distributed Syst., vol. 2, no. 4, pp. 398–412, Oct. 1991.
W.C. Athas and C.L. Seitz, “Multicomputers: Message-passing concurrent computers,” IEEE Comput. Mag., vol. 21, no. 8, pp. 9–24, Aug. 1988.
P.E. Berman, L. Gravano, G.D. Pifarré and J.L.C. Sanz, “Adaptive deadlock-and livelock-free routing with all minimal paths in torus networks,” in Proc. 4th ACM Symp. Parallel Algorithms Architectures, June 1992.
R.V. Bopana, and S. Chalasani, “A comparison of adaptive wormhole routing algorithms,” in Proc. 20th Annu. Int. Symp. Comput. Architecture, May 1993.
S. Borkar et al., “iWarp: An integrated solution to high-speed parallel computing,” in Proc. Supercomputing'88, Nov. 1988.
A.A. Chien and J.H. Kim, “Planar-adaptive routing: Low-cost adaptive networks for multiprocessors,” in Proc. 19th Annu. Int. Symp. Comput. Architecture, May 1992.
A.A. Chien, “A cost and speed model for k-ary n-cube wormhole routers,” in Proc. Hot Interconnects'93, Aug. 1993.
W.J. Dally and C.L. Seitz, “The torus routing chip,” Distributed Comput., vol. 1, no. 3, pp. 187–196, Oct. 1986.
W.J. Dally and C.L. Seitz, “Deadlock-free message routing in multiprocessor interconnection networks,” IEEE Trans. Comput., vol. C-36, no. 5, pp. 547–553, May 1987.
W.J. Dally, “Virtual-channel flow control,” IEEE Trans. Parallel Distributed Syst., vol. 3, no. 2, pp. 194–205, Mar. 1992.
W.J. Dally and H. Aoki, “Deadlock-free adaptive routing in multicomputer networks using virtual channels,” IEEE Trans. Parallel Distributed Syst., vol. 4, no. 4, pp. 466–475, April 1993.
J. Duato, “On the design of deadlock-free adaptive routing algorithms for multicomputers: design methodologies,” in Proc. Parallel Architectures Languages Europe 91, June 1991.
J. Duato, “Deadlock-free adaptive routing algorithms for multicomputers: evaluation of a new algorithm,” in Proc. 3rd IEEE Int. Symp. Parallel Distributed Processing, Dec. 1991.
J. Duato, “A new theory of deadlock-free adaptive routing in wormhole networks,” IEEE Trans. Parallel Distributed Syst., vol. 4, no. 12, pp. 1320–1331, Dec. 1993.
J. Duato, “A necessary and sufficient condition for deadlock-free adaptive routing in wormhole networks,” in Proc. Int. Conf. Parallel Processing, Aug. 1994.
P.T. Gaughan and S. Yalamanchili, “Adaptive routing protocols for hypercube interconnection networks,” IEEE Comput. Mag., vol. 26, no. 5, pp. 12–23, May 1993.
D. Gelernter, “A DAG-based algorithm for prevention of store-and-forward deadlock in packet networks,” IEEE Trans. Comput., vol. C-30, pp. 709–715, Oct. 1981.
C.J. Glass and L.M. Ni, “The turn model for adaptive routing,” in Proc. 19th Annu. Int. Symp. Comput. Architecture, May 1992.
C.J. Glass and L.M. Ni, “Maximally fully adaptive routing in 2D meshes,” in Proc. Int. Conf. Parallel Processing, Aug. 1992.
K.D. Gunther, “Prevention of deadlocks in packet-switched data transport systems,” IEEE Trans. Commun., vol. COM-29, pp. 512–524, Apr. 1981.
C.R. Jesshope, P.R. Miller, and J.T. Yantchev, “High performance communications in processor networks,” in Proc. 16th Annu. Int. Symp. Comput. Architecture, May–June 1989.
P. Kermani and L. Kleinrock, “Virtual cut-through: a new computer communication switching technique,” Comput. Networks, vol. 3, pp. 267–286, 1979.
J. Kim, A.Chien, “An evaluation of the planar/adaptive routing,” in Proc. 4th IEEE Int. Symp. Parallel Distributed Processing, 1992.
S. Konstantinidou, L. Snyder, “Chaos router: Architecture and performance,” in Proc. 18th Annu. Int. Symp. Comput. Architecture, May 1991.
H.T. Kung, “Deadlock avoidance for systolic communication,” in Proc. 15th Annu. Int. Symp. Comput. Architecture, May–June 1988.
X. Lin and L.M. Ni, “Deadlock-free multicast wormhole routing in multicomputer networks,” in Proc. 18th Annu. Int. Symp. Comput. Architecture, May 1991.
X. Lin, P.K. McKinley and L.M. Ni, “The message flow model for routing in wormhole-routed networks,” in Proc. 1993 Int. Conf. Parallel Processing, Aug. 1993.
Z. Liu, J. Duato and L.-E. Thorelli, “Grouping virtual channels for deadlock-free adaptive wormhole routing,” in Proc. Parallel Architectures Languages Europe 93, June 1993.
D.H. Linder and J.C. Harden, “An adaptive and fault tolerant wormhole routing strategy for k-ary n-cubes,” IEEE Trans. Comput., vol. C-40, no. 1, pp. 2–12, Jan. 1991.
P. López and J. Duato, “Deadlock-free adaptive routing algorithms for the 3D-torus: limitations and solutions,” in Proc. Parallel Architectures Languages Europe 93, June 1993.
P.K. McKinley, H. Xu, A. Esfahanian and L.M. Ni, “Unicast-based multicast communication in wormhole-routed networks,” in Proc. 1992 Int. Conf. Parallel Processing, Aug. 1992.
P.M. Merlin and P.J. Schweitzer, “Deadlock avoidance in store-and-forward networks — I: Store-and-forward deadlock,” IEEE Trans. Commun., vol. COM-28, pp. 345–354, Mar. 1980.
P.R. Miller, “Efficient communications for fine-grain distributed computers,” Ph.D Thesis, Southamptom University, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Duato, J., López, P. (1994). Performance evaluation of adaptive routing algorithms for k-ary n-cubes. In: Bolding, K., Snyder, L. (eds) Parallel Computer Routing and Communication. PCRCW 1994. Lecture Notes in Computer Science, vol 853. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58429-3_27
Download citation
DOI: https://doi.org/10.1007/3-540-58429-3_27
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58429-2
Online ISBN: 978-3-540-48787-6
eBook Packages: Springer Book Archive